Probe with a virtual marker

ABSTRACT

A probe for use in a coordinate digitizing system includes an indicator, such as a pointing tip or crosshairs, and a marker, the location of which can be determined by a marker tracking system relative to a coordinate system. The probe is configured to effectively place the marker&#39;s virtual image—as seen by the tracker—at the same location as the indicator without blocking a user&#39;s view of the indicator.

FIELD OF THE INVENTION

The present invention relates to methods and systems for opticallymeasuring and locating points on two-dimensional surfaces or inthree-dimensional volumes.

BACKGROUND OF THE INVENTION

Methods and systems for capturing coordinates of points—or locations—ofreal-world surfaces for input into computer-aided design (CAD) softwareare in widespread use. The points may be on a two-dimensional (2D)surface or on the exterior of a three-dimensional (3D) object. Theprocess of inputting coordinates of points of a 2D medium or a 3D objectinto a computer memory is commonly called digitizing. For example, adigitizing tablet may be used to input XY coordinates of sampled pointson a 2D image—such as a photograph, blueprint, or pencil-sketcheddrawing—in order to build a CAD or other computer graphicsrepresentation of the salient geometric features of the image.

Similarly, a “cloud of points” may be sampled from the 3D surface of aphysical object to build a data representation (or model) of thegeometry of the physical object in a computer memory. Each sampled pointmay be represented by an XYZ coordinate triple. In a more sophisticatedrepresentation, the cloud of points may be converted into vertices ofabutting planar polygonal patches which approximate the surface of theobject. In a more sophisticated representation, the cloud of points maybe converted into abutting curved polygonal patches. Each patch, whetherplanar or curved, may be defined by a mathematical bivariate polynomialor rational function—such as in the NURBS surfaces commonly used incomputer graphics. In special cases, 3D data entry may rely onreal-world measurements where the generic geometric shape (e.g., circle,sphere, cube, cylinder, etc.) of a real-world object is known, but thedimensions of the shape must be determined by physically measuring thecoordinates of one or more points to quantify the shape.

Numerous approaches exist for measuring real-world surface points. Forplanar media, various 2D digitizing tablets are commercially availablewhich are commonly used in computer-aided drafting and design. The twomost common input devices are a hand-held pen-like stylus with apointing tip, and a manually moveable cursor—also called a puck. Themovable cursor may have a reticle scribed into a transparent plate whichcan be moved over the surface of the tablet or a planar medium on thetablet. A common form of a reticle is pair of crosshairs. The reticlemay include an indicator, such as an arrow tip or the intersection ofthe crosshairs, which indicates the particular surface point to bemeasured by the moveable cursor.

A probe may be used to input of points on the surface of a 3D object.Such a probe may have a pointer, tip, or other indicator for indicatingan individual location on the object. The indicator may be a sharpconical pointer, a spherical tip of known radius, a grooved tip fortracing edges, or a roller of known radius.

Generally, the location of the indicator on the probe, cursor, or puckis measured in two or three dimensions by a coordinate measuring system,referred to herein as a tracker. The tracker may not track the indicatordirectly, but instead track sensible markers spaced apart from theindicator. In many cases, placing a sensible marker exactly at thelocation of the indicator would be problematic, because the size or theopacity of the marker may obscure the indicator from view. This problemmay be avoided by tracking two or more markers positioned with a knowngeometrical relationship with respect to the indicator, so the locationof the indicator may be computed from the locations of the markers.

SUMMARY OF THE INVENTION

The various embodiments provide methods and systems for measuring a 2Dor 3D location in a coordinate system using only one marker on a probe.The probe contains an indicator to designate the location of a specificpoint on a 2D surface or in a 3D volume for the measurement of thelocation. A single trackable marker on the probe effectively has thesame location as the indicator without blocking a user's view of theindicator. An embodiment measures the location of the marker with atracker, which may report the location as 2D or 3D coordinates in acoordinate system.

An embodiment is configured so that the indicator lies at a known offsetand at a constrained direction from the marker. An embodiment for aplanar or 2D application positions the marker and the indicator on thesame line normal (perpendicular) to the surface. An embodiment for 3Dapplications uses the known offset and direction of the marker tocompute the location of the indicator in the plane of the medium.

Another embodiment virtually collocates a probe's marker and indicatorby using a mirror—or an equivalent reflecting surface for a sonicmarker. In this embodiment, the indicator and the marker lie on oppositesides of the mirror's reflecting surface at equal distances from thereflecting surface and on a line perpendicular to the reflectingsurface. This configuration causes the location of a virtual image ofthe marker to coincide with the location of the indicator. Inalternative embodiments, the mirror may be planar or non-planar.

A portion of the probe including the marker and the mirror may be hingedor moveable as long as the image of the marker continues to coincidewith the indicator.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated herein and constitutepart of this specification, illustrate presently preferred embodimentsof the invention, and, together with the general description given aboveand the detailed description given below, serve to explain features ofthe invention.

FIG. 1 is a perspective view of an embodiment of a probe for 2D input.

FIG. 2 is a perspective view of an embodiment of a probe without amarker reflector (mirror).

FIG. 3A is a side cross-sectional view of a probe embodiment having amagnifying lens.

FIG. 3B is a rear cross-sectional view of the embodiment shown in FIG.3A.

FIG. 3C is a cross-section view from the side of a probe embodimenthaving a periscope to view the indicator.

FIG. 3D is a side cross-sectional view of a probe embodiment having abent, magnifying optical fiber image conduit.

FIG. 4 is a diagram illustrating how the image of a marker is made tovirtually coincide with the indicator.

FIGS. 5A and 5B are drawings of two 3D optical trackers with alternativelocations for photodiodes.

FIG. 6A is a cross-sectional view of a probe embodiment having a movablemarker and mirror assembly.

FIGS. 6B and 6C are front and side views respectively of an alternativeprobe embodiment having a moveable marker and mirror assembly.

FIGS. 7A and 7B are front and side cross-sectional views respectively ofanother alternative embodiment with a moveable marker and mirrorassembly

FIG. 8 is a perspective view of a probe for use in indicating a point ona 3D surface.

FIG. 9 is a cross-sectional diagram illustrating how the image of amarker is made to virtually coincide with the indicator using a curvedmirror.

FIG. 10A is a side cross-sectional view of a probe embodiment having asecondary marker.

FIG. 10B is a rear cross-sectional view of the same embodiment as shownin FIG. 10A.

FIG. 11 is a perspective view of a probe with two secondary markers.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Various embodiments of the present invention will be described in detailwith reference to the accompanying drawings. Wherever possible, the samereference numbers will be used throughout the drawings to refer to thesame or like parts.

Generally, the location of the indicator of a probe of a 2D digitizingtablet or a 3D tracking system is measured relative to a coordinatesystem. The coordinate system typically may be a standard Cartesian(rectangular) coordinate system, possibly defined by the user withrespect to the medium or object being digitized. The location of theindicator of a probe relative to the coordinate system is typicallydetermined by a marker coordinate measurement system, referred to hereinas a tracker. For digitizing points on a plane, the tracker typicallyreports the location of the indicator of a 2D probe as numerical X and Ycoordinates. An example of a 2D tracker is a planar digitizing tablet,which may be constructed with marker location sensing wires buried inthe digitizing tablet. A family of such tablets is available from WacomTechnology Corp. (Vancouver, Wash.). For digitizing points in a 3Dvolume, the tracker typically reports the location of the indicator of a3D probe as X, Y, and Z coordinates. An example of a handheld, opticallytracked probe and its 3D tracker are the FlashPoint and 3D Creatorproducts sold by Boulder Innovation Group, Inc. (Boulder, Colo.).

Both 2D and 3D probes generally incorporate at least one localized,trackable, physically sensible marker. Each sensible physical marker isa feature which defines a reference point on the probe. A marker may bea point-like light source, a light detector, a retro-reflector, ahigh-contrast target pattern, a sound emitter, a magnetic coil, oranother sensible physical feature. The location of each marker may bemeasured essentially continuously by the tracker. For example, eachmarker may have an optical characteristic, such as an illuminated spothaving a centroid, the location of which is precisely measured by anoptical tracker. Optical trackers may measure the marker location usingvisible, infrared or ultraviolet spectra. Other types of trackersmeasure the location of a marker on a 2D surface or in a 3D volume usingultrasound or magnetic fields instead of light.

A reticle of a cursor and the pointing tip of a probe both are referredto herein as an indicator. The stylus, cursor, or puck for 2D digitizingand the probe used for 2D or 3D digitizing are referred to as a probe.Each probe includes an indicator that indicates the specific, singlepoint on which the indicator lies or which the indicator contacts at agiven moment.

It has often been impractical to locate a single sensible marker atexactly the same location on the probe as the indicator. One reason isthat markers, being generally opaque, would block a user's view of theindicator if collocated with the indicator. That is, the indicatoreffectively would be inside and at the very center of the marker. Thus,the marker make it difficult for the user to position the indicator onthe point to be measured (i.e., digitized). Aside from visibilityproblems, the physical volume of the marker would prevent the user fromtouching the indicator directly to the point to be digitized. Forexample, some optical trackers use a retro-reflective one-centimeterball as a marker. That size marker would completely envelop andoptically block the indicator if the indicator and marker werepositioned concentrically on the probe. To resolve this problem, manyprobes include markers located some distance from the indicator to allowa user to visually place the indicator of the probe at a desired pointfor measurement. A tracker can measure the location of the marker andthen compute the location of the indicator given the known offset anddirection.

Many trackers only measure the location of a marker and not itsorientation, especially when the marker is omni-directional, such as asingle light-emitting diode (LED) or a retro-reflective ball.Consequently, a tracker cannot determine the location of the indicatorbased on the location of an omni-directional marker since it cannotdetermine the rotational orientation of the probe (and thus the offsetdirection of the marker with respect to the indicator). Therefore, aprobe employing such markers generally requires at least twospaced-apart markers for 2D measurements and at least three spaced-apartmarkers for 3D measurements. Using the known relationship of the markersto the indicator and from the measured coordinates of the multiplemarkers, the coordinates of the indicator may be computed usingwell-known techniques of analytic geometry.

For example, there may be at least two markers at known distances fromthe indicator of the probe. Then, a tracker may compute the spatialcoordinates of the indicator given the measured coordinates of the twomarkers. More generally, there may be three or more markers in knowngeometric relationships to the indicator. Techniques for computing thecoordinates of the indicator from the measured coordinates of at leastthree markers are well known to persons of ordinary skill in the art of2D or 3D digitizing. Commercial 2D digitizing tablets and 3D trackersand their probes regularly employ multiple markers on a probe forcomputing the location coordinates of the indicator on the probe.

Nevertheless, it can be advantageous to use only one marker on a probe.For example, some trackers do not measure the location coordinates ofmultiple markers at exactly the same moment. With such trackers, anymotion of the probe between measurements can introduce error into thecomputation of the indicator location. Using only one marker on theprobe with the marker collocated with the indicator can avoid sucherrors.

FIG. 1 shows an embodiment of a probe 30 for use in digitizing points ofinterest on a planar medium or other surface 12 in conjunction with atracker 20 coupled to a computer 50 by a data cable 40 (or wireless datalink). The probe 30 is positioned on points to be digitized so thecoordinates of the points can be measured by determining the position ofa marker using a 2d or 3D tracker 20. For example, the probe 30 may beused to indicate and measure sample points along a line 11 inconjunction with the 3D tracker 20 to generate XY coordinates of theline 11 for storage in a computer 50. In this example, the surface 12may be assumed to coincide with the XY plane of the 3D coordinate system19. In such a configuration, an XY coordinate system can be used forrecording coordinates of the line 11 as is typical for 2D digitizingapplications. A 3D tracker 20 may provide a set-up feature which allowsa user to define the origin and the X and Y axes so that the coordinatesystem corresponds to the surface 12. In that situation, the Zcoordinates of the locations of the probe 30 may be ignored ordiscarded. An example of a tracker 20 is the FlashPoint system ofBoulder Innovation Group (Boulder, Colo.), which provides two functions(the OXY and XXY commands) that enable a user to define such a customcoordinate system.

Alternatively, a reference frame 49 with its own sensible markers may beattached to the surface 12 and measured by the tracker 20 to registerthe coordinate system 19 of the tracker 20 with respect to the markersof the reference frame 49. Thereafter, as long as the reference frame 49remains fixed, the coordinate system of the tracker 20 remains fixedwith respect to the reference frame 49, and therefore fixed with respectto the surface 12. This remains true even when the tracker 20 is movedwith respect to the surface 12. To register the tracker 20,

In use, the tracker 20 records the coordinates of one or more points ofthe surface 12 and communicates this information via a data cable 40 tothe computer 50 for storage. Recording may conditionally take place whenthe user presses a button (41 in FIG. 2) on the probe 30 (whose signalmay be conveyed to the computer 50 by a data cable 40), depresses a footswitch, gives a verbal command, or otherwise instructs the system tomeasure and record (digitize) a point or sequence of points to thecomputer 50. The computer 50 may collect and record the coordinates ofthe points in order to construct a CAD model, for example.

The tracker 20 illustrated in FIG. 1 may be an optical tracker. It mayemploy two or more video cameras in a conventional stereo arrangement.Alternatively, the tracker 20 may employ three linear charge-coupleddevices (CCDs), such as used by the aforementioned Flashpoint system. Inanother embodiment, the tracker 20 may track point-like sources ofsound, in which case the tracker 20 may include an array of microphones.In another embodiment, the tracker 20 may generate nutating magneticfields which orthogonally oriented coils in the marker 30 can sense.Information from the marker coils may be communicated by a data cable 40(or wireless data link) to the computer 50 from which the computer 50can derive the location and orientation of the indicator. Withoutimplying limitation, further descriptions of digitizing systems will bebased upon optical trackers 20.

FIG. 2 shows an embodiment of a probe 30 that includes a housing 36supporting a top cap 42 and a transparent base plate 35 having anindicator 31 in the form of crosshairs scribed thereon. A marker 32,such as a light or retroflector ball, may be positioned in the top cap42 in line with the indicator 31. Also, the probe 30 may include abutton 41 and signal generation circuitry for signaling when acoordinate measurement should be taken, coupled to a data cable 40 forsending signals from the button 41 to the computer 50. The probe mayalso include a status light 44 on the end cap 42 for indicating a statusof the probe.

In an embodiment, the indicator 31 is scribed on the bottom of thetransparent plate 35 so there can be no angular disparity between thelocation of the intersection of the indicator 31 and the point directlyunder the indicator 31. In this embodiment, the transparent plate 35 maybe glass or plastic. In an alternative embodiment, the base plate 35 maybe a thin slab of optical fiber image conduit, which optically raisesthe image of the surface 12 to the top of the base plate 35, so theindicator 31 may be scribed on the top of the base plate 35. In thisembodiment, the optical fiber image conduit prevents any refractiveshift (disparity) between the image of the surface 12 under the baseplate 35 and the indicator 31.

During use of the probe 30, the base plate 35 and the indicator 31 arein contact with a surface 12 to be measured. The marker 32 is at a knownoffset from the indicator 31 and on the line from the indicator 31perpendicular to the plane of the base plate 35. The marker 32 is offsetfrom (e.g., positioned above) the indicator 31 in order not block theline-of-sight between the indicator 31 and a user. The offset enablesthe user 1 to place the indicator 31 of the probe 30 at the clearlyvisible location on the surface 12. The tracker 20 can determine the XYcoordinates of the indicator 31 by measuring the coordinates of themarker 32 and by compensating for the known offset in the perpendiculardirection of the marker with respect to the indicator 31.

The probe 30, shown as a puck in FIG. 2, includes a structural housing36 to maintain the fixed geometric relationship between the indicator 31and the marker 32. A part of the housing 36 may be transparent or opento provide ambient light to the indicator 31 and the surface 12 so as toallow the user 1 to see the indicator 31 and the underlying image beingdigitized.

The button 41 on the probe 30 may be pressed to control when XYcoordinate measurements are made. Any well known switch circuit (notshown separately) may be mechanically coupled to the button 41, so thatwhen a user pressing the button, an electrical signal (e.g., closing acircuit) is generated. In an embodiment, button 41 may be coupled todigital circuits to generate a digital signal in response to a userpressing the button. The button and associated switch circuitry areconnected to communication circuitry so that the signal can betransmitted to the computer, such as by means of the data cable 40. In asimple embodiment, the communication circuitry is a simple conductor sothat when the button is pressed, closing the switch circuitry,electrical energy is communicated through the conductor through the datacable 40 to the computer. In another embodiment, the communicationcircuitry is a digital communication bus configured to convey a digitalsignal from the switch circuitry to the data cable 40. In a furtherembodiment in which data is transmitted wirelessly instead of by meansof a data cable 40, the communication circuitry includes a wireless datalink transceiver as are well known in the art that is configured toreceive a digital signal from the switch circuitry and communicate theinformation in the signal to the computer wirelessly. In use, when theprobe 30 is centered on a particular point, a user presses the button 41which in conjunction with associated switch and communication circuitrysends a signal to the computer indicating that a location measurement ofthe marker 32 should be taken.

The probe 30 may include a status light 44, such as an LED, or an audiotransducer (not shown) to inform the user of success or failure of aparticular coordinate measurement. To provide this functionality, thecomputer 50 may activate status light 44 by sending signals via the datacable 40. For example, the computer 50 may cause the status light 44 toflash to inform the user of a problem, such as blocked line-of-sightbetween the marker 32 and the tracker 20. The cable 40 may also providepower to the marker 32. The data cable 40 may be electrical or optical,and may be unidirectional or bidirectional.

In an alternative embodiment, communication between the probe and thecomputer 50 may be by way of a wireless data link (not shown as it isinvisible). Such a wireless link may transmit and/or receive radiowaves, infrared, sound, some other wireless medium, or a combinationthereof to communicate information to and from the computer 50. Theprobe 30 may include a self-contained energy source, such as a battery(not shown) for powering the status light 44, marker 32 (if necessary)and data communication circuitry.

The marker 32 may be any of a variety of sensible marker. The marker 32may be an active, point-like source of light, such as a light-emittingdiode (LED), which may flash or emit light continuously. An LED may emitan infrared or visible wavelength. The marker 32 may be a smallretro-reflective spot or ball, in which case there may be one or moresources of light on or near the tracker 20 to illuminate the marker 32.The marker 32 may be a passive, distinctively-colored or high-contrastshape or pattern, lit only by ambient light. An example of such apassive pattern is the checkered pattern tracked by the Micron Trackerof Claron Technologies (Toronto, Ontario, Canada). For an ultrasonictracker 20, the marker 32 may be a piezoelectric crystal or a spark gapwhich emit sounds. For a magnetic tracker 20, the marker 32 may be a setof three tiny orthogonal induction coils.

As illustrated in FIG. 2, an embodiment is configured to position theindicator 31 at a known offset distance from the marker 32 and at aconstrained direction with respect to the base plate 35. For a planar or2D application, the probe 30 may position the marker 32 and theindicator 31 on the same line perpendicular to the surface 12 (i.e.,positioning the marker 32 directly above the indicator 31). This designmaintains a constant offset direction of the marker 32 even as the probe30 is rotated around the perpendicular while the indicator 31 maintainscontact with a specific point on the surface 12. Being positioned on topof the probe 30, the marker 32 can be tracked in three dimensions, whilethe known offset and direction can be used to compute the location ofthe indicator 31 in the plane of the surface 12. In particular, if thecoordinate system is defined so the surface 12 lies in the XY plane,then the indicator 31 lies on the XY plane while the marker 32 lies in aparallel plain offset by its elevation- or non-zero Z coordinate. Thusin this embodiment, the indicator 31 and the marker 32 have the same XYcoordinates. The Z coordinate of the marker 32 may be ignored or set tozero to yield the coordinates of the indicator 31. If the coordinatesystem is not defined so that the surface 12 lies in the XY plane, wellknown analytic geometry methods can be used to project the coordinatesof the marker 32 perpendicularly onto the plane of the surface 12 toyield the coordinates of the indicator 31.

FIGS. 3A and 3B show cross-section views of another embodiment of aprobe 30. In this embodiment, the probe 30 is configured to collocate avirtual image of a marker 32 and the indicator by using a mirror 33properly placed to create the virtual image. To avoid doublereflections, the mirror 33 preferably is a first-surface mirror. A prismwith internal reflection may also be used instead of a mirror 33. Theindicator 31 and the marker 32 lie on opposite sides of the reflectingsurface of the mirror 33 at equal distance from the reflecting surfaceof the mirror 33, and on a line 5 perpendicular to the reflectingsurface of the mirror 33. An observation line 3 extends from the marker32, is reflected in the mirror 33 and detected by a light sensor orcamera 21 a of the tracker 20. The reflection of the marker 32 creates avirtual image which appears at the end of line 6, which is the virtualcontinuation of the line-of-sight from the tracker 20 to the virtualimage of the marker 32. The probe 30 is further configured so that auser can observe the indicator 31, such as illustrated by a ray of lightfollowing line 2 from the indicator 31 to the user eye 1. Because of thegeometrical relationship between the indicator 31 and the marker 32provided by the configuration of the probe 30, the apparent location ofthe virtual image of the marker 32 as viewed by the tracker 20 coincideswith the actual location of the indicator 31 as observed the user.Therefore, the tracker 20 measures the location of the marker 32 asbeing at the same location as the indicator 31. Accordingly, there is noneed to calculate the coordinates of the indicator 31 to account for anoffset of the marker 32.

The embodiment illustrated in FIGS. 3A and 3B may include any or all ofthe following: a transparent base plate 35, a housing 34, a statusindicator 44, and a button (not shown). The housing 34 may include asource of illumination 47 for illuminating the marker 32—if it is apassive marker—and/or a source of illumination 46 for illuminating theindicator 31. Further, the embodiment may include a window or magnifier,such as a lens 37, through which the user can observe the indicator 31.The lens 37 may be removable. The embodiment may include a transparentprotective cover 45 to protect the mirror 33 from dust, scratches,fingerprints, or smudges, while allowing the tracker 20 to observe themirror 33. A sliding shutter, removable cap, or a protective coating(not shown) on the mirror 33 may be used instead of or in addition to atransparent protective cover 45.

To prevent the tracker 20 from seeing both the reflected virtual imageof the marker 32 and the marker 32 itself, there may need to be one ormore appropriately-placed opaque baffles or opaque portions of thehousing 34. The top of the probe 30 housing 34 may be opaque, serving assuch a baffle and obstructing the direct line of sight between thetracker 20 and the marker 32. The marker 32 may be mounted on the bottomside of the baffle or housing 34. The tracker 20 may include a lightsource 47 for illuminating the marker 32 via the mirror 33, enabling theuse of a retro-reflective marker 32.

Another embodiment of a probe 30 is illustrated in FIG. 3C. Like theembodiment shown in FIGS. 3A and 3B, a mirror 33 is configured withinthe probe 30 to present a virtual image of the marker 32 to the tracker20 which is coincident with the location of the indicator 31. In thisembodiment, an arrangement of periscope mirrors 38A and 38B provides theuser with a better view of the indicator 31, which may not otherwise bedirectly visible to the user's eye 1. Instead of mirrors 38A, 38B, theperiscope may be constructed with one or more prisms, such as apentaprism similar to that used in a single-lens reflex camera. Anembodiment may employ a transparent window instead of a lens 37 toprotect the periscope mirrors 38 and/or the base plate 35 from dust,scratches, fingerprints, or smudges. Alternatively, a sliding shutter,removable cap, or a protective coating on the base plate 35 and/or onthe periscope mirrors 38 may be used instead of or in addition to atransparent window or a lens 37.

The embodiment illustrated in FIG. 3C allows the user to view theindicator 31 without obstruction while the tracker 20 observes a virtualimage of the marker 32 in the same location. Thus, as with theembodiment described above, the tracker 20 measures the location of themarker 32 directly with no need to calculate coordinates of theindicator 31 to account for an offset of the marker 32.

Another embodiment is illustrated in FIG. 3D. This embodiment providesthe user with a better view of the indicator 31 by using an opticalfiber image conduit 39 acting as both the lens 37 and the base plate 35.The amount of magnification provided the optical fiber image conduit 39depends on the relative taper between the distal end which contacts thesurface 12 and the proximal end closest to the user's eye 1. Anembodiment may use a combination of a lens 37, periscope mirrors 38A,38B or prisms, and/or an optical fiber image conduit 39 to enhancevisibility of the indicator 31 by the user 1. It should be appreciatedthat a periscope configuration and an image conduit 39 not only allow auser to view an image of the indicator 31 and the surface 12, but theyalso convey ambient light in to illuminate the indicator 31 and thesurface 12.

Paths of light emanating from a marker 32 in the direction of a tracker20 are illustrated in FIG. 4. As illustrated, light from the marker 32is reflected in the mirror 33 to create a virtual image of the marker 32that effectively coincides with the physical location of the indicator31. Light from the marker 32 travels along the lines 3, reflecting offthe mirror 33. Because the angle of incidence equals the angle ofreflection, the marker 32 appears to tracker 20 to be located behind themirror 33 at the location of the indicator 31. Since the indicator 31and marker 32 are positioned equal distance from the reflecting surfaceof the mirror 33 along a line 5 perpendicular to the mirror 33, thevirtual image of the marker 32 at the location of the indicator 31 willbe the same distance from the reflecting surface of the mirror 33 as themarker 32 is from the reflecting surface. Therefore, the tracker 20 willmeasure the location of the virtual image of the marker 32 at thelocation of the indicator 31.

It should be noted that a similar probe configuration can be providedfor an ultrasonic tracker, in which the equivalent of the mirror 33 maybe a hard, sound-reflecting surface, and the sonic equivalent of anoptical baffle may be a soft, deeply textured surface such as foam. Likelight, sound from an ultrasound marker will be reflected off thesound-reflecting surface to create a virtual sonic source.

Some optical 3D trackers 20 may experience problems in circumstanceswhere the line-of-sight to a marker is partially blocked by anintervening object. In such situations the optical tracker 20 mayincorrectly measure the location of the marker. For example, if themarker is an LED or a retro-reflective ball, there may be an error inthe measured coordinates because the centroid of the portion visible tothe tracker 20 is offset from the actual center of the marker. For aone-centimeter retro-reflective ball, the positional error may be morethan a millimeter. This problem may also occur with the probeembodiments described herein, such as, for example, when the user's handpartially blocks the line-of-sight from one of the cameras 21 a-21 c ofthe tracker 20 to the virtual image of the marker 32. However,conventional trackers 20 may not be able to detect this circumstance andwarn the user.

For the probes described herein, there is an addition problematiccircumstance in which the virtual image of the marker 32 can bepartially blocked. The probe may be oriented so that the virtual imageof the marker 32, as observed by a camera 21 a-21 c of the tracker 20,is reflected off the edge of the mirror 33. In such circumstances theimpact on positional accuracy may be the same as when an interveningobject partially blocks the line-of-sight to a marker 32.

An embodiment of a tracker 20 includes provisions to detect a partiallyblocked line-of-sight to a marker 32 or to the virtual image of a marker32. Specifically, photodetectors 27 (which may be photodiodes) may beincluded on the tracker 20 for use with markers that are active LEDs orretro-reflective balls. FIGS. 5A and 5B show two embodiment arrangementsfor mounting a plurality of photodetectors 27 on an optical tracker 20which also includes two or more cameras 21 a, 21 b, and 21 c. Thecameras may each be conventional 2D video cameras or linear CCDs, forexample. The photodetectors 27 function to detect when a marker 32 (suchas an LED or a retro-reflective spot), or the virtual image of a marker32 may be partially blocked from the sight of at least one camera 21 a,21 b, or 21 c. When the marker 32 is partially blocked by the edge ofsome intervening object, at least one photodetector 27 will receivelittle or no light from the marker 32. The photodetectors 27 can detectthis decrease in light and signal the tracker 20 (or the computer 50) toindicate that some partial blockage of light exists. This function willalso detect situation in which the marker 32 is only partiallyreflected, such a because the virtual image of the marker 32, as seen bythe tracker 20, falls at the edge of the mirror 33.

For example, if a marker 32 is partially blocked, at least one camera 21a, 21 b, or 21 c is likely to see only part of the marker 32 while atleast one other camera 21 a, 21 b, or 21 c will see the entire marker.Similarly, the photodetectors 27 will detect unequal intensities oflight, as may be determined by circuits which compare the intensitiesdetected by at least two photodetectors 27. Because the photodetectors27 are mounted slightly outward from the cameras 21 a, 21 b, 21 c, thephotodetectors may detect a problematic circumstance before the cameras21 a, 21 b, 21 c are affected. If all the photodetectors 27 receiveapproximately the same intensity of light from a marker 32, then ingeneral all cameras will see the entire marker 32. When at least twophotodetectors 27 receive substantially different light intensities, thetracker 20 can warn the user of a potentially inaccurate measurement,such as by causing the status light 44 to flash. Similarly, thephotodetectors 27 can detect partial blockage of the virtual image of amarker 32. While the photodetectors are optional, they may be used towarn the user of potentially inaccurate results in these problematiccircumstances.

Because of the practical area of the mirror 33 may be limited, theembodiments described previously may have a limited range of angles inwhich the virtual image of the marker 32 in the mirror 33 is fullyvisible to the tracker 20. This visibility limitation may be partiallyaddressed by moving or rotating the tracker 20 to a different viewpoint,but that may not be convenient or possible while maintaining thecoordinate system. To address this limitation, alternative embodimentsmay be used which have better virtual image visibility. Theseembodiments operate on the same principle as the foregoing embodimentsby maintaining three geometric relationships between the indicator 31,the marker 32, the mirror 33 and the tracker 20:

1. The marker 32 and the indicator 31 have the same distance from theplanar reflecting surface of the mirror 33;

2. The line between the marker 32 and the indicator 31 is perpendicularto the reflecting surface of the mirror 33; and

3. The image of the marker 32 in the mirror, though not the marker 32itself is be directly visible to the tracker 20.

These geometric relationships can be maintained even if part of theprobe 30 is hinged or moveable with respect to the base plate 35 or tothe rest of the probe 30.

A first of these alternative embodiments is illustrated in FIG. 6A whichmaintains the above geometric relationships. This embodiment includes astructural base 63 with a spherical bearing portion 63A whichaccommodates a marker support 61 suspended by leaf springs 64. Atransparent base plate 35 connected to the bottom of the structural base63 includes an indicator 31. While the structural base 63, thetransparent base plate 35, and the indicator 31 remain in contact withthe surface 12, the marker support 61 may be moved within the sphericalbearing portion 63A so that the marker 32 can trace a portion of asphere even as the geometric relationships listed above are maintained.Specifically, the indicator 31 and the marker 32 remain equidistant fromthe mirror 33, the line between the indicator 31 and the marker 32remains perpendicular to the mirror 33, and the marker 32 cannot be seendirectly by the tracker 20, because the marker 32 faces the mirror 33. Aleaf or cup spring 64 keeps the spherical bearing portion of the markersupport 61 in contact with the mating spherical portion of thestructural base 63 by pushing against a pin 67. While the structuralbase 63 and the indicator 31 remain fixed, the marker support 61 may berotated and moved to an orientation where the tracker 20 gets anunobstructed view of the virtual image of the marker 32.

Another probe embodiment is illustrated in which includes semicirculararc 65 coupled to the transparent base plate 35 which includes anindicator 31, and slider 66 coupled to the semicircular arch 65 and amarker 32, a mirror 33 configured to maintain the geometricrelationships described above. In this embodiment, the slider 66includes a marker support 61 that keeps the marker 32 at a constantdistance from the mirror 33. The slider 66 maintains contact with thecircular arch 65 so that the mirror 33 remains at a constant distancefrom indicator 31 at the center of the circular arch 65. The slider 66is designed with guides or grips to keep it in contact with the arch 65as the slider is moved along the arch 65. The slider 66 and the markersupport 61 insure that the marker 32 and the indicator 31 areequidistant from the reflecting surface of mirror 33 and the line 5between the marker 32 and the indicator 31 remains perpendicular to themirror 33. Thus, the arch 65, slider 66, and marker support 61 insurethat the geometric relationships described above are maintained as theslider 66 and marker support 61 are moved along the arch 65. As such,the embodiment insures that the virtual image of the marker 32 as viewedby a tracker 20 always coincides with the physical location of theindicator 31. While the arch 65 and the indicator 31 remain fixed, themarker support 61 can be moved to an angle where the tracker 20 can havean unobstructed view of the virtual image of the marker 32.

The embodiments illustrated in FIGS. 6A through 6C may use transparentglass or plastic base plate 35 with an indicator 31. Alternatively, thebase plate 35 may be slab of an optical fiber image conduit which avoidsrefraction which can otherwise shift the apparent location of theindicator 31 and/or points on the surface 12 as the user shifts viewingperspective.

A further embodiment of a probe 30 is illustrated in FIGS. 7A and 7B.This embodiment employs a hinge-like articulated mechanical arrangementin which a hinged mirror and marker support 61 rotates about the axis ofhinge pins 62. The axis of the hinge pins 62 intersects the indicator31. Because the pins are above the surface 12, the base plate 35 is anoptical fiber image conduit, which in effect optically raises the pointson surface 12, including the indicator 31, to the level of the axis ofthe pins 62. The hinge pins 62 on the mirror and marker support 61insures that the marker 32 and the indicator 31 are equidistant from thereflecting surface of mirror 33 and the line 5 between the marker 32 andthe indicator 31 remains perpendicular to the mirror 33. Thus, thisembodiment maintains the geometric relationships described above.Accordingly, the virtual image of the marker 32 coincides with theindicator 31 because all light rays 3 emitted from marker 32 reachingthe tracker 20 appear to originate from the location of the indicator31. While the base 63 and the indicator 31 remain fixed, the mirror andmarker support 61 may be moved to an angle where the tracker 20 can havean unobstructed view of the virtual image of the marker 32.

While the foregoing embodiments are intended for use on a planar surface12, base plate 35 (or the structural base 63) of a probe 30 need not beplanar if the base plate 35 (or the structural base 63) has a surfaceshape which matches a non-planar measurement surface 12. For example, ifthe measurement surface 12 is spherical with a radius R, the base plate35 may have a mating spherically concave surface with a radius R. Such aprobe 30 may be useful in manually designating a location on a globe,for example. Similarly, if the surface 12 is cylindrical, the base plate35 (or the structural base 63) may have a mating, cylindrical curvature.

A further embodiment appropriate for indicating points on a 3D surfaceis illustrated in FIG. 8. This probe embodiment satisfies the samegeometric relationships as described above. Specifically, the probe 30has an indicator 31 in the form of a sharp pointing tip, a marker 32,and a mirror 33 arranged so that the indicator 31 and marker 32 areequidistant from the reflective surface of the mirror 33 and positionedalong a line perpendicular to the mirror 33. Consequently, the virtualimage of marker 32 appears to coincide with the indicator 31 because alllight rays 3 emitted from marker 32 reaching tracker 20 appear tooriginate from the location of the indicator 31 along the virtual ray 6.The marker 32 may be oriented to face the mirror 33, so that it cannotbe observed directly by tracker 20.

An alternative embodiment of the probe 30 may replace the sharp pointingindicator tip with a spherical tip of known radius. In this case, theindicator 31 is the center of the sphere. The probe 30 would be used inthe same way as a spherical sensing tip on a coordinate measuringmachine (CMM). That is, the indicator 31 at the center of a sphere neveractually touches the surface of some 3D object which is being digitizedbut maintains a constant distance from the surface. Subsequent softwareprocessing adjusts the measured coordinates to account for the offset ofthe center of the spherical tip from its surface. Digitizing surfacesusing a probe with a spherical tip is well known in the art of 3Dcoordinate measurement.

In the various embodiments, the mirror 33 need not be planar. Instead, acurved mirror 33A may be used as illustrated in FIG. 9. As shown, lightfrom the marker 32 travels along the lines 3, reflecting off the mirror33A. However, to the tracker 20, the light appears to come from theindicator 31 where the virtual image of the marker 32A appears,traveling along the lines 5. The geometric relationships listed above donot hold for a non-planar mirror. Instead, the marker 32 will be placedat a location with respect to the curved mirror so that its virtualimage optically appears to be at the same location as the indicator 31.The distance between the marker 32 and the curved mirror 33A will notequal the distance between the indicator 31 and the curved mirror, andinstead the distances will depend on the curvature of the mirror 33A.Persons of ordinary skill in optics can design the mirror 33A and choosethe distances so that the location of the virtual image is invariant andcoincides with the indicator 31 regardless of where the tracker 20 islocated. Using a curved mirror may provide more compact optical paths soa probe 30 having a curved mirror may be more compact. Although thecurved mirror 33A shown in FIG. 9 is concave, a convex mirror may beused instead. The mirror 33A may be a section of a sphere, paraboloid oranother curved surface. The mirror 33A may be a first-surface mirror toavoid secondary reflections. It should be noted that the virtual imageof the marker 32 in a curved mirror will not be the same size as theactual marker 32 A. For some kinds of trackers 20, this change in sizemay be problematic. For example, a retro-reflective ball may appearlarger or smaller than expected. To address this problem, the size ofthe marker may be adjusted so that the virtual image of the marker isthe proper size.

The probe embodiments described so far require only one marker 32 to betracked. Since the virtual image of the marker 32 is tracked and appearsto be exactly at the physical location of the indicator 31, no furthermarkers are required for determining the location of the indicator 31.Consequently, the foregoing probe embodiments are shown as beingcircular in configuration since their rotational orientation is not ofsignificance. However, if the probe 30 is not rotationally symmetricalfor a 2D application (e.g., it can point in the direction of a line aswell as reveal the location of a point on the line) or additionalinformation is required regarding the shape of a 3D object (e.g., thenormal to the surface) the tracker 20 must be able to determine theangular orientation of the probe 30 as well as the location of theindicator 31. To enable the tracker 20 to obtain this additionalinformation, at least one more marker 32 a on the probe 30 may berequired. The additional marker or markers 32 a, 32 b are referred toherein as secondary markers, while the marker 32 whose virtual imagecoincides with the indicator 31 is referred to herein as the primarymarker.

For example, FIGS. 10A and 10B illustrate probe 30 embodiment whichincludes two secondary markers 32 a, 32 b. The markers 32 a, 32 b arelocated on the probe 30 in positions which enable the tracker 20 todetermine the probe's rotational orientation, such as one secondarymarker 32 a on top of the housing 34 and another secondary marker 32 belsewhere on the housing 34. The secondary markers 31 a, 32 b may bespaced apart from the virtual image of the primary marker 32 and fromeach other in order to enable the tracker 20 to resolve and measure therelative positions of each marker.

The location coordinates of the virtual image of the marker 32 and asingle secondary marker 32 b may be used to determine the orientation ofthe probe in a 2D coordinate system. In a 3D coordinate system, at leasttwo secondary markers 32 a and 32 b are required in order to determineits position and orientation with respect to the three dimensions ofspace plus the three rotational orientations (i.e., pitch, roll and yaw)that the probe 30 can assume. The secondary markers 32 a or 32 b neednot be reflected in the mirror 33 since there is no need to create avirtual image of the markers in order to avoid obscuring the indicator31. It should be noted that although the primary marker 32 and thesecondary marker 32 a are shown as being physically located close toeach other in FIGS. 10A and 10B, the virtual image of the primary marker32 as seen by the tracker 20 is at the indicator 31, and thus will beseen as well removed from the secondary marker 32 a.

When two or more secondary markers 32 a and 32 b are positioned on aprobe 30, it may be advantageous to provide a way for the tracker 20 todistinguish among them. One way to distinguish multiple markers 32, 32a, and 32 b is to insure that they form an irregular pattern so that themeasured locations of all the markers 32, 32 a, and 32 b can exactlymatch only one orientation. Another way to distinguish among markers isto make them appear different to the tracker 20, such as by means ofcolor, shape or other feature. For example, if the markers 32, 32 a, 32b are active LEDs, the LEDs may be flashed in a predetermined sequenceor at times controlled by the tracker 20 to uniquely identify eachmarker. These and other ways of distinguishing markers commonly known incommercially available trackers 20 may be used.

In an embodiment, the probe may be configured so that the tracker canview both the primary marker 32 itself and the virtual image of theprimary marker 32 (i.e., the marker 32 as observed in the mirror 33) toprovide two separate, spaced-apart markers. In this embodiment, thevirtual image of the marker 32 will appear at the same location as theindicator 31, while the marker 32 itself will be imaged at its actuallocation. For example, in the probe 30 shown in FIGS. 10A and 10B, themarker 32 may simply protrude through the top baffle or housing 34 toalso double as the secondary marker 32 a.

For each of the single marker embodiments described above, at least onesecondary marker 32 a or 32 b may be added. For example, the embodimentillustrated in FIGS. 10A and 10B is very similar to the embodimentillustrated in FIGS. 3A and 3B except for the addition of the secondarymarkers 32 a and 32 b.

Besides providing orientation information, the secondary markers 32 amay also be used to verify the measurements of the primary marker 32.For example, the computed distances between the measured locations ofall the markers (primary and secondary) may be compared to the knowndistances between the markers on a probe 30. If the distances betweenthe measured marker separations differ from the known distances by morethan a small tolerance, then a measurement problem is indicated. Suchconsistency checks are well known to persons of ordinary skill in theart of optical digitizing.

Further, the orientation information provided by the secondary markersmay be used to compensate for known orientation-related systematicerrors-especially in 3D applications. For example, FIG. 11 illustratesan embodiment with a primary marker 32 and two secondary markers 32 aand 32 b. The three markers 32, 32 a, 32 b are not collinear, so the 3Dspatial orientation of the probe 30 may be determined by the tracker 20.If the mirror 33 is not a first-surface mirror, the distance of thevirtual image of the marker 32 may vary slightly depending on theorientation angle of the mirror 33 relative to the tracker 20. Theorientation angle may be represented as the angle between a light ray 3and the plane of the mirror 33. By determining the orientation of theprobe 30, the tracker 20 (or the attached computer 50) may compensatefor the effect of refraction on the apparent location of the virtualimage may be estimated by means of Snell's Law with the result used tocompute a correction to the apparent location to generate the actuallocation of the indicator 31.

While the present invention has been disclosed with reference to certainpreferred embodiments, numerous modifications, alterations, and changesto the described embodiments are possible without departing from thesphere and scope of the present invention, as defined in the appendedclaims. Accordingly, it is intended that the present invention not belimited to the described embodiments, but that it have the full scopedefined by the language of the following claims, and equivalentsthereof.

1. A method for measuring a location of an indicator on a probe,comprising: providing a marker and a mirror, wherein the mirror has acurved reflective surface; forming a virtual image of the marker behindthe mirror, where the virtual image has an image location; maintaining afixed relative relationship among the marker, the indicator and themirror, wherein the image location of the virtual image coincides withthe location of the indicator; measuring the image location of thevirtual image of the marker using a tracker; and representing thelocation of the indicator with coordinates based on the image locationof the virtual image of the marker.
 2. The method of claim 1, whereinmaintaining a fixed relative relationship among the marker, theindicator and the mirror includes mounting the marker, the indicator,and the mirror on a probe in a fixed geometric relationship to eachother.
 3. The method of claim 2, further comprising allowing at leasttwo parts of the probe to move relative to each other.
 4. The method ofclaim 1, further comprising providing a source of illumination for themarker.
 5. The method of claim 1, further comprising providing a baffleto prevent direct measurement of the marker by the tracker.
 6. Themethod of claim 1, further comprising: measuring a location of asecondary marker positioned on the probe in a fixed relationship to themirror, the virtual image of the marker, and the indicator; anddetermining a spatial orientation of probe based upon the measuredlocations of the image location of the virtual image of the marker, themeasured location of the secondary marker and the fixed relationship. 7.A probe for indicating a location to a tracker, comprising: an indicatoron the probe for indicating a location; an optical fiber image conduitconfigured to provide a view of the indicator; a marker on the probe;and a reflective surface on the probe for forming a virtual image of themarker, wherein the indicator, marker, and reflective surface arepositioned on the probe and configured so that a location of the virtualimage of the marker can be measured by the tracker and the location ofthe virtual image of the marker coincides with the location of theindicator.
 8. The probe of claim 7, wherein the reflective surface isprovided by a prism.
 9. The probe of claim 7, wherein the reflectivesurface comprises a mirror.
 10. The probe of claim 9, wherein the mirroris a first-surface mirror.
 11. The probe of claim 7, wherein the markeris an optical marker that can be imaged by the tracker.
 12. The probe ofclaim 7, further comprising a periscope configured to provide a view ofthe indicator.
 13. The probe of claim 7, further comprising a source ofillumination for the marker.
 14. The probe of claim 7, furthercomprising a baffle to prevent direct measurement of the marker by thetracker.
 15. The probe of claim 7, wherein the probe is configured sothat the marker and reflective surface can move around an axis ofrotation but the location of the virtual image of the marker remainscoincident with the location of the indicator.
 16. The probe of claim 7,further comprising a secondary marker having a location on the probewhich the tracker can measure that is in a fixed geometric relationshipto the reflective surface, the virtual image, and the indicator, therebyindicating a spatial orientation of the probe.
 17. A method formeasuring a location of an indicator on a probe, comprising: providing amarker and a mirror; providing a periscope for viewing the indicator,forming a virtual image of the marker behind the mirror, where thevirtual image has an image location; maintaining a fixed relativerelationship among the marker, the indicator and the mirror, wherein theimage location of the virtual image coincides with the location of theindicator; measuring the image location of the virtual image of themarker using a tracker; and representing the location of the indicatorwith coordinates based on the image location of the virtual image of themarker.
 18. The method of claim 17, wherein maintaining a fixed relativerelationship among the marker, the indicator and the mirror includesmounting the marker, the indicator, and the mirror on a probe in a fixedgeometric relationship to each other.
 19. The method of claim 18,further comprising allowing at least two parts of the probe to moverelative to each other.
 20. The method of claim 17, wherein the mirroris replaced with a prism.
 21. The method of claim 17, further comprisingproviding a source of illumination for the marker.
 22. The method ofclaim 17, further comprising providing a baffle to prevent directmeasurement of the marker by the tracker.
 23. A method for measuring alocation of an indicator on a probe, comprising: providing a marker anda mirror; forming a virtual image of the marker behind the mirror, wherethe virtual image has an image location; maintaining a fixed relativerelationship among the marker, the indicator and the mirror, wherein theimage location of the virtual image coincides with the location of theindicator; measuring the image location of the virtual image of themarker using a tracker; providing a baffle to prevent direct measurementof the marker by the tracker; and representing the location of theindicator with coordinates based on the image location of the virtualimage of the marker.
 24. The method of claim 23, wherein maintaining afixed relative relationship among the marker, the indicator and themirror includes mounting the marker, the indicator, and the mirror on aprobe in a fixed geometric relationship to each other.
 25. The method ofclaim 24, further comprising allowing at least two parts of the probe tomove relative to each other.
 26. The method of claim 23, wherein themirror is replaced with a prism.
 27. The method of claim 23, furthercomprising providing a source of illumination for the marker.
 28. Amethod for measuring a location of an indicator on a probe, comprising:providing a marker and a mirror; forming a virtual image of the markerbehind the mirror, where the virtual image has an image location;maintaining a fixed relative relationship among the marker, theindicator and the mirror, wherein the image location of the virtualimage coincides with the location of the indicator; measuring the imagelocation of the virtual image of the marker using a tracker;representing the location of the indicator with coordinates based on theimage location of the virtual image of the marker; measuring a locationof a secondary marker positioned on the probe in a fixed relationship tothe mirror, the virtual image of the marker, and the indicator; anddetermining a spatial orientation of probe based upon the measuredlocations of the image location of the virtual image of the marker, themeasured location of the secondary marker and the fixed relationship.29. The method of claim 28, wherein maintaining a fixed relativerelationship among the marker, the indicator and the mirror includesmounting the marker, the indicator, and the mirror on a probe in a fixedgeometric relationship to each other.
 30. The method of claim 29,further comprising allowing at least two parts of the probe to moverelative to each other.
 31. The method of claim 28, wherein the mirroris replaced with a prism.
 32. The method of claim 28, further comprisingproviding a source of illumination for the marker.
 33. A probe forindicating a location to a tracker, comprising: an indicator on theprobe for indicating a location; a periscope configured to provide aview of the indicator; a marker on the probe; and a reflective surfaceon the probe for forming a virtual image of the marker, wherein theindicator, marker, and reflective surface are positioned on the probeand configured so that a location of the virtual image of the marker canbe measured by the tracker and the location of the virtual image of themarker coincides with the location of the indicator.
 34. The probe ofclaim 33, wherein the reflective surface is provided by a prism.
 35. Theprobe of claim 33, wherein the reflective surface comprises a mirror.36. The probe of claim 33, wherein the marker is an optical marker thatcan be imaged by the tracker.
 37. The probe of claim 36, wherein theprobe is configured so that the marker and reflective surface can movearound an axis of rotation but the location of the virtual image of themarker remains coincident with the location of the indicator.
 38. Aprobe for indicating a location to a tracker, comprising: an indicatoron the probe for indicating a location; a marker on the probe; a baffleto prevent direct measurement of the marker by the tracker; and areflective surface on the probe for forming a virtual image of themarker, wherein the indicator, marker, and reflective surface arepositioned on the probe and configured so that a location of the virtualimage of the marker can be measured by the tracker and the location ofthe virtual image of the marker coincides with the location of theindicator.
 39. The probe of claim 38, wherein the marker is an opticalmarker that can be imaged by the tracker.
 40. The probe of claim 38,wherein the probe is configured so that the marker and reflectivesurface can move around an axis of rotation but the location of thevirtual image of the marker remains coincident with the location of theindicator.
 41. A probe for indicating a location to a tracker,comprising: an indicator on the probe for indicating a location; amarker on the probe; a reflective surface on the probe for forming thevirtual image of the marker, wherein the indicator, marker, andreflective surface are positioned on the probe and configured so that alocation of the virtual image of the marker can be measured by thetracker and the location of the virtual image of the marker coincideswith the location of the indicator; and a secondary marker having alocation on the probe which the tracker can measure that is in a fixedgeometric relationship to the reflective surface, the virtual image, andthe indicator, thereby indicating a spatial orientation of the probe.42. The probe of claim 41, wherein the probe is configured so that themarker and reflective surface can move around an axis of rotation butthe location of the virtual image of the marker remains coincident withthe location of the indicator.